Problem: Solve for $x$ and $y$ using elimination. ${-4x-y = -24}$ ${-3x+y = -11}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-y$ and $y$ cancel out. $-7x = -35$ $\dfrac{-7x}{{-7}} = \dfrac{-35}{{-7}}$ ${x = 5}$ Now that you know ${x = 5}$ , plug it back into $\thinspace {-4x-y = -24}\thinspace$ to find $y$ ${-4}{(5)}{ - y = -24}$ $-20-y = -24$ $-20{+20} - y = -24{+20}$ $-y = -4$ $\dfrac{-y}{{-1}} = \dfrac{-4}{{-1}}$ ${y = 4}$ You can also plug ${x = 5}$ into $\thinspace {-3x+y = -11}\thinspace$ and get the same answer for $y$ : ${-3}{(5)}{ + y = -11}$ ${y = 4}$